Proposals to improve maths teachers’ pay, put forward this week in a report which painted a picture of a subject in crisis, have been rejected by unions.

Headteacher and classroom associations said the move would be difficult to justify, even if it was extended to all shortage subjects.

Professor Adrian Smith, leader of the government task force which wrote the report, urged ministers to re-examine the issue in the face of an estimated fall of 3,400 in qualified maths staff since 1996.

Vacancy rates were consistently higher than in any other subject. Maths teachers also had lower-grade degrees than other subject teachers.

Professor Smith suggested that pound;5,000 extra be added to salaries.

But David Hart, general secretary of the National Association of Head Teachers, said: “Why should you pay an averagely performing maths teacher more than an excellent English teacher?”

John Dunford, general secretary of the Secondary Heads Association, said many maths teachers were already getting more than their colleagues as heads paid more to attract them.

Differential pay for maths and science teachers was first proposed by the Roberts Review on science education in 2002. The idea was rejected by the School Teachers’ Review Body, which said they should not be singled out for special treatment.

Professor Smith’s report suggests an alternative: that maths teachers be paid extra in return for completing professional development courses.

Professor Smith, principal of Queen Mary college, London, also suggested ministers should consider waiving tuition fees for all maths undergraduates.

The report said pupils and teachers had been let down by a succession of mistakes, from the “complete disaster” of bungled exam reforms to inadequate official data on the number of maths teachers.

Maths GCSEs and A-levels were failing to give employers and universities basic guarantees that students have mastered the subject, the 15-month inquiry found.

Professor Smith concluded:

* GCSEs are demotivating the 30 per cent of candidates who take the foundation tier, where the best grade they can achieve is a C. They also fail to stretch the most able 10 per cent.

* The Curriculum 2000 reforms, which launched AS-levels, were an “utter and complete disaster”, resulting in a 15 per cent fall in maths entries.

* Vocational courses are so confusing that even he struggled to grasp their complexities.

Professor Smith said many employers were telling him that a GCSE grade B or C signified “virtually nothing” in terms of a pupil’s knowledge.

It was difficult to pick out the real high-flyers from those who got A-grade GCSEs. A grade B could be achieved by pupils who had not mastered algebra and geometry.

Professor Smith said pupils had to sit too many exams and that league tables were damaging the subject. He said the modular system favoured by many subjects, was “inappropriate within maths as a discipline”.

The 172-page report welcomed the near doubling in the number of maths recruits to teacher training in the past five years. But targets were still not being met. It was difficult to compile definitive figures on teacher supply, however, because the Government had no detailed data beyond 1996.

The report said that maths should be made into a “double GCSE”, worth two passes, to reflect the effort required. Statistics should be studied in biology and geography courses instead.

In the long term, 14 to 16-year-olds should be offered at least five separate courses, or pathways, ranging from basic “maths for the citizen” to advanced work.

From 16, students would take one of seven pathways, including one on “public understanding of maths”, looking at the role of mathematical ideas in human culture. The detail will be worked out by Mike Tomlinson’s 14-19 review. Schools may be contributing to the shortage of maths teachers by allowing staff who graduated in the subject to take on managerial roles, the report concludes.

Figures from 1996 indicated that one in four secondary teachers with a qualification in the subject was not teaching it. The report also revealed that the maths strand of the key stage 3 strategy had taken 300 experienced secondary maths teachers out of schools since 2001 to act as advisers.

Professor Smith called for a “maths tsar” to champion the subject. He said he found it “astonishing” that many of his conclusions were echoes of those from as long ago as 1982, in the Cockcroft report on maths teaching.

Union leaders welcomed many of the report’s findings. The Association of Teachers and Lecturers describing the recommendations as a “wake-up call” for ministers.

The Maths Association said that Profressor Smith had not said enough about how pressure from targets and league tables was damaging teaching.

David Miliband, the school standards minister, said the Government had put maths at the top of its agenda since 1997. Ministers are not saying how long they will take to respond.

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ACTION POINTS

* Extra pay for maths teachers, possibly linked to training

* Professional development entitlement written into maths teachers’ contracts

* Double maths GCSE to be introduced as soon as possible

* Statistics to be removed from maths GCSE

* New GCSE structure to give all students chance of a grade C

* Extension courses for the most able students at GCSEA-level

* Split the subject into five courses at14 to 16 and into seven post-16

* National centre of excellence for maths teaching

* Maths tsar to champion the subject.